In a rhythm game the difference between a 10ms ping (wired average for just audio) and a 100-300ms ping (Bluetooth average for just audio) is definitely noticeable, at any level of play. With Bluetooth it isn't even just 1 frame you'll miss, it's about a 3rd of a second in the worst case.

This isn't necessarily a fair comparison because USB receiver headsets latency much closer to wired exist, but most people with wireless headsets will be using Bluetooth, and not aptX LL Bluetooth.

I don't even play rhythm games, casually playing the music-synced rooms in Celeste (a 2D platformer) was enough to make me stop playing until I could find a wire for my Sony XM5's.